
\begin{tikzpicture}[scale=1.3]
  \def\Ax{0} \def\Ay{5} \def\Bx{3} \def\By{0} \def\Cx{0} \def\Cy{0}
  \coordinate[label=below left:$C$] (C) at (\Cx,\Cy);
  \coordinate[label=left:{$A(0, b)$}] (A) at (\Ax,\Ay);
  \coordinate[label=below right:{$B(a, 0)$}] (B) at (\Bx,\By);
  \coordinate[label=right:$D$] (D) at ($ (A)!(C)!(B) $);
  \path[name path=AI] (A) -- ({\calcbisectorx\Cx\Cy\Ax\Ay\Bx\By},0);
  \path[name path=BJ] (B) -- (0,{\calcbisectory\Ax\Ay\Bx\By\Cx\Cy});
  \path[name path=DI] (D) -- ($ (D)!2/3! -45:(C) $);
  \path[name path=DJ] (D) -- ($ (D)!1/2! 45:(C) $);
  \path[name intersections={of=AI and DI}]
    coordinate[label=above right:$I$] (I) at (intersection-1);
  \path[name intersections={of=BJ and DJ}]
    coordinate[label=above:$J$] (J) at (intersection-1);
  \path[name path=IK] (I) -- ($ (I)!17/11!(J) $);
  \path[name path=BC] (B) -- (C);
  \path[name intersections={of=IK and BC}]
    coordinate[label=below:$K$] (K) at (intersection-1);
  \pic[mark angle={blue}{3mm}{1}] {right angle=B--C--A};
  \pic[mark angle={blue}{3mm}{1}] {right angle=A--D--C};
  \pic[mark angle={red}{4mm}{1}] {angle=I--K--C};
  \pic[mark angle={cyan}{8mm}{1.5}, "$\alpha$"] {angle=C--A--I};
  \pic[mark angle={cyan}{8mm}{2}, "$45^\circ - \beta$"] {angle=B--C--J};
  \pic[mark angle={teal}{4mm}{1.5}, "$\beta$"] {angle=J--B--C};
  \pic[mark angle={teal}{6mm}{1.5}, "$45^\circ - \alpha$"] {angle=I--C--A};
  \draw (A) -- (B) -- (C) -- cycle (C) -- (D) (I) -- (K);
  \draw[dashed] (A) -- (I) (C) -- (I) (B) -- (J) (C) -- (J);
  \draw[very thick, ->] (-.2,0) -- (3.2,0) node[above] {$x$};
  \draw[very thick, ->] (0,-.2) -- (0,5.2) node[right] {$y$};
\end{tikzpicture}
